用廣義斐波那契數(shù)及其產(chǎn)生方法進行圖的哈密頓圈的計數(shù)
ENUMERATING ALL HAMILTONIAN CYCLES IN SOME GRAPHS BY USING THE GENERALIZED FIBONACCI SEQUENCE AND ITS PRODUCTION RULE
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摘要: 本文首先對斐波那契數(shù)進行推廣,然后對文獻[1]中提出的遞推算法進行了抽象,找到了可以描述這一算法的產(chǎn)生式和遞推關(guān)系,從而首次求得了兩種最大平面圖中哈密頓圈的計數(shù)公式。
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關(guān)鍵詞:
Abstract: In this paper the Fibonacci sequence is generalized at first. Then the algorithm which has been published in this Journal by the author and his colleague is developed. Both production and recursion formulas for describing the algorithm are obtained. Here the two formulas for enumerating all hamiltonian cycles in two kinds of maxi-mum planar graphs seem to be derived for the first time. -
金綏更、江炳堯,電子學通訊,4(1982), 191.[2]F. Harary著,李慰萱譯,圖論,上?？萍汲霭嫔?1980.[4]D. E. Knuth著,管紀文、蘇運霖譯,計算機程序設(shè)計技巧,國防工業(yè)出版社,1980.[8]S. L. Hakimi and E. F. Schmeichel, J. of Graph Theory, 3(1979),69. -
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